Mathematical Sciences: Control and Stabilization Problems for a Class of Nonlinear Partial Differential

小行星9402838 该项目涉及的分析和计算研究的全球（在状态空间）控制和稳定问题的Korteweg -德弗里斯和相关的偏微分方程。将考虑点（边界）和分布式控制模式。先进的计算和符号处理能力，将采用在调查中的保守法律的闭环过程，以获得先验的解决方案的界限。这将允许受控系统的瞬态和渐近行为的仔细分析。 Korteweg - de弗里斯和其他相关的非线性偏微分方程的解典型地包括孤波，称为孤子。 这些波出现在许多应用中，包括气象学和海洋学，光纤信号传输，化学运输和扩散过程等。 感兴趣的问题，这将是在这个项目中进行的研究，包括孤立波的能量衰减，孤立波的稳定创建，并分析中继器型放大孤立波。这项研究将包括调查和基于计算机的过程模拟过程的数学分析。

9402838 Russell This project involves analytical and computational studies of global (in the state space) control and stabilization problems for the Korteweg - de Vries and related partial differential equations. Both point (boundary) and distributed control modes will be considered. Advanced computational and symbolic processing capabilities will be employed in the investigation of conservation laws for closed loop processes in order to obtain a priori bounds on solutions. This will permit a careful analysis of the transients and asymptotic behavior of the controlled system. Solutions of the Korteweg - de Vries, and other, related, nonlinear partial differential equations characteristically include solitary waves, called solitons. These waves occur in numerous applications, including meteorology and oceanography, fiber-optic signal transmission, chemical transport and diffusion processes, and many others. Questions of interest which will be addressed by the research to be undertaken in this project include energy attenuation in solitary waves, stable creation of solitary waves, and analysis of repeater type amplification of solitary waves. This research will include both mathematical analyses of the processes under investigation and computer based process simulation.